There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sqrt(x)ln(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(x)sqrt(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(x)sqrt(x)\right)}{dx}\\=&\frac{sqrt(x)}{(x)} + \frac{ln(x)*\frac{1}{2}}{(x)^{\frac{1}{2}}}\\=&\frac{sqrt(x)}{x} + \frac{ln(x)}{2x^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{sqrt(x)}{x} + \frac{ln(x)}{2x^{\frac{1}{2}}}\right)}{dx}\\=&\frac{-sqrt(x)}{x^{2}} + \frac{\frac{1}{2}}{x(x)^{\frac{1}{2}}} + \frac{\frac{-1}{2}ln(x)}{2x^{\frac{3}{2}}} + \frac{1}{2x^{\frac{1}{2}}(x)}\\=&\frac{-sqrt(x)}{x^{2}} - \frac{ln(x)}{4x^{\frac{3}{2}}} + \frac{1}{x^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-sqrt(x)}{x^{2}} - \frac{ln(x)}{4x^{\frac{3}{2}}} + \frac{1}{x^{\frac{3}{2}}}\right)}{dx}\\=&\frac{--2sqrt(x)}{x^{3}} - \frac{\frac{1}{2}}{x^{2}(x)^{\frac{1}{2}}} - \frac{\frac{-3}{2}ln(x)}{4x^{\frac{5}{2}}} - \frac{1}{4x^{\frac{3}{2}}(x)} + \frac{\frac{-3}{2}}{x^{\frac{5}{2}}}\\=&\frac{2sqrt(x)}{x^{3}} + \frac{3ln(x)}{8x^{\frac{5}{2}}} - \frac{9}{4x^{\frac{5}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2sqrt(x)}{x^{3}} + \frac{3ln(x)}{8x^{\frac{5}{2}}} - \frac{9}{4x^{\frac{5}{2}}}\right)}{dx}\\=&\frac{2*-3sqrt(x)}{x^{4}} + \frac{2*\frac{1}{2}}{x^{3}(x)^{\frac{1}{2}}} + \frac{3*\frac{-5}{2}ln(x)}{8x^{\frac{7}{2}}} + \frac{3}{8x^{\frac{5}{2}}(x)} - \frac{9*\frac{-5}{2}}{4x^{\frac{7}{2}}}\\=&\frac{-6sqrt(x)}{x^{4}} - \frac{15ln(x)}{16x^{\frac{7}{2}}} + \frac{7}{x^{\frac{7}{2}}}\\ \end{split}\end{equation} \]

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